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Simplifying 0 = -16t2 + 32t + 240 Reorder the terms: 0 = 240 + 32t + -16t2 Solving 0 = 240 + 32t + -16t2 Solving for variable 't'. Combine like terms: 0 + -240 = -240 -240 + -32t + 16t2 = 240 + 32t + -16t2 + -240 + -32t + 16t2 Reorder the terms: -240 + -32t + 16t2 = 240 + -240 + 32t + -32t + -16t2 + 16t2 Combine like terms: 240 + -240 = 0 -240 + -32t + 16t2 = 0 + 32t + -32t + -16t2 + 16t2 -240 + -32t + 16t2 = 32t + -32t + -16t2 + 16t2 Combine like terms: 32t + -32t = 0 -240 + -32t + 16t2 = 0 + -16t2 + 16t2 -240 + -32t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -240 + -32t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-15 + -2t + t2) = 0 Factor a trinomial. 16((-3 + -1t)(5 + -1t)) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-3 + -1t)' equal to zero and attempt to solve: Simplifying -3 + -1t = 0 Solving -3 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1t = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1t = 0 + 3 -1t = 0 + 3 Combine like terms: 0 + 3 = 3 -1t = 3 Divide each side by '-1'. t = -3 Simplifying t = -3Subproblem 2
Set the factor '(5 + -1t)' equal to zero and attempt to solve: Simplifying 5 + -1t = 0 Solving 5 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1t = 0 + -5 -1t = 0 + -5 Combine like terms: 0 + -5 = -5 -1t = -5 Divide each side by '-1'. t = 5 Simplifying t = 5Solution
t = {-3, 5}
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